Methodological notes

Coherent and semiclassical states of a free particle

 a,  b, a, c,  d
a Tomsk State University, prosp. Lenina 36, Tomsk, 634050, Russian Federation
b Lebedev Physical Institute, Russian Academy of Sciences, Leninsky prosp. 53, Moscow, 119991, Russian Federation
c Universidade de São Paulo, Instituto de Física, São Paulo, Brazil
d Universidade de São Paulo, R.daReitoria 109, São Paulo, 05508-900, Brazil

Coherent states (CS) were first introduced and studied in detail for bound motion, discrete spectrum system like the harmonic oscillator and similar systems with a quadratic Hamiltonian. However, the problem of constructing CS has not yet received detailed investigation for the simplest and physically important case of a free particle for which, besides being physically important, the CS problem is of didactic value in teaching quantum mechanics where CSs can be considered as examples of wave packets representing semiclassical motion. In this paper we follow essentially the Malkin—Dodonov—Man’ko method to construct the CS of a free nonrelativistic particle. We give a detailed discussion of the properties of the CSs obtained, in particular, the completeness relations, the minimization of uncertainty relations and the evolution of the corresponding probability density. We describe the physical conditions under which free particle CSs can be considered as semiclassical states.

Fulltext is available at IOP
PACS: 03.65.−w
DOI: 10.3367/UFNe.0184.201409c.0961
Citation: Bagrov V G, Gitman D M, Pereira A S "Coherent and semiclassical states of a free particle" Phys. Usp. 57 891–896 (2014)
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Received: 29th, January 2014, 26th, March 2014

:   ,   ,    «   » 184 961–966 (2014); DOI: 10.3367/UFNr.0184.201409c.0961

References (18) ↓ Cited by (14) Similar articles (20)

  1. Klauder J R, Sudarshan E C G Fundamentals Of Quantum Optics (New York: W.A. Benjamin, 1968)
  2. Klauder J R, Skagerstam B-S Coherent States: Applications In Physics And Mathematical Physics (Singapore: World Scientific, 1985)
  3. Perelomov A Generalized Coherent States And Their Applications (Berlin: Springer-Verlag, 1986); Perelomov A M Obobshchennye Kogerentnye Sostoyaniya i Ikh Primeneniya (M.: Nauka, 1987)
  4. Gazeau J-P Coherent States In Quantum Physics (Weinheim: Wiley-VCH, 2009)
  5. Nielsen M A, Chuang I L Quantum Computation And Quantum Information (Cambridge: Cambridge Univ. Press, 2000)
  6. Malkin I A, Man’ko V I Dinamicheskie Simmetrii i Kogerentnye Sostoyaniya Kvantovykh Sistem (M.: Nauka, 1979)
  7. Dodonov V V, Man’ko V I "Invarianty i korrelirovannye sostoyaniya nestatsionarnykh kvantovykh sistem" Invarianty i Evolyutsiya Nestatsionarnykh Kvantovykh Sistem (Trudy FIAN) Vol. 183 (Pod red. M A Markova) (M.: FIAN, 1987) p. 71; Dodonov V V, Man’ko V I "Invariants and correlated states of nonstationary quantum systems" Invariants And The Evolution Of Nonstationary Quantum Systems (Proc. of the Lebedev Physics Institute) Vol. 183 (Ed. M A Markov) (Commack, NY: Nova Science, 1989) p. 71
  8. Dodonov V V, Man’ko V I (Eds) Theory Of Nonclassical States Of Light (London: Taylor & Francis, 2003)
  9. Littlejohn R G Phys. Rep. 138 193 (1986)
  10. de la Torre A C, Goyeneche D M arXiv:1004.2620
  11. Guerrero J et al. J. Phys. A Math. Theor. 44 445307 (2011)
  12. Geloun J B, Hnybida J, Klauder J R J. Phys. A Math. Theor. 45 085301 (2012)
  13. Gitman D M, Tyutin I V, Voronov B L Self-adjoint Extensions In Quantum Mechanics. General Theory And Applications To Schrödinger And Dirac Equations With Singular Potentials (Progress in Mathematical Physics) Vol. 62 (New York: Birkhäuser, 2012)
  14. Bagrov V G, Gitman D M Exact Solutions Of Relativistic Wave Equations (Mathematics and Its Applications (Soviet Series)) Vol. 39 (Dordrecht: Kluwer Acad. Publ., 1990)
  15. Schrödinger E Sitzungsber. Preuß. Akad. Wiss. Berlin Math. Phys. 19 296 (1930); Translated into English, Schrödinger E Bulg. J. Phys. 26 193 (1999); Schrödinger E quant-ph/9903100
  16. Robertson H P Phys. Rev. 35 667 (1930)
  17. De Alfaro V, Regge T Potential Scattering (Amsterdam: North-Holland Publ., 1965)
  18. Bagrov V G et al. J. Phys. A Math. Theor. 44 055301 (2011)

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